In T. K. Truong, L. J. Wang, I. S. Reed, and W. S. Hsieh, “Image data compression using cubic convolution spline interpolation,” IEEE Trans. on Image Processing, vol. 9, no. 11, pp. 1988–1995, November 2000 [1]; and L. J. Wang, W. S. Hsieh, T. K. Truong, I. S. Reed, and T. C. Cheng, “A fast efficient computation of cubic-spline interpolation in image codec,” IEEE Trans. on Signal Processing, vol. 49, no. 6, pp. 1189–1197, June 2001 [2], the entire contents of which are hereby expressly incorporated by reference, a cubic spline interpolation (CSI) is developed in order to subsample image data to achieve compression. The CSI scheme is combined with the JPEG algorithm to develop a modified JPEG encoder-decoder, which obtains a higher compression ratio and a better quality of reconstructed image than the standard JPEG In the CSI algorithm developed in [1], a fast Fourier transform (FFT) algorithm used in the modified JPEG encoder, is applied to perform the circular convolution needed to compress and reconstruct image data.
Recently, the authors in [2] showed that if the size of compressed image is not chosen to be power of two, the usual 2-D FFT is not the best algorithm needed to obtain the compressed image values. To overcome this problem, the authors proposed the Winograd discrete Fourier transform (WDFT) with the overlap-save method instead of the FFT to implement the CSI scheme. The disadvantage of this faster CSI algorithm is the overlap-save method with its required boundary conditions. Thus this algorithm though faster is not readily realized as a real-time processor.
Therefore, there is a need for a method and apparatus for a faster and more efficient computation of a CSI for image signals.